# NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

**NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables- **In previous classes, you have studied linear equations in one variable. In this particular chapter, you will study linear equations in two variables of the type ax+by+c=0 where a, b and c are the real numbers, and a and b both are not zero. NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables are there to make your task easy while preparing for the exams. In this chapter, there are a total of 4 exercises which consist of 16 questions. NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables is covering the detailed solutions to each and every question present in the practice exercises. This is an important chapter as this created a foundation for the higher level of algebra. Algebra is a unit in class 9 maths which holds 20 marks in the final examination. This chapter always comes with a good number of questions in competitive exams like the Indian National Olympiad (INO), National Talent Search Examination (NTSE). NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables are designed in such a manner that a student can get maximum marks assigned to that particular question. NCERT solutions are also available classwise and subject wise which can be downloaded by clicking on the given link. Here you will get NCERT solutions for class 9 also.

## ** NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.1 **

** Answer: **

Let the cost of a notebook be Rs * x * and that of a pen be Rs * y * .

According to the given condition: The cost of a notebook is twice the cost of a pen.

Thus,

### ** Answer: **

Given :

Here , a=2, b=3 and c =

### ** Answer: **

Given:

Here ,

a=1,

c = -10

### ** Answer: **

Given :

Here , a= -2, b=3 and c = -6

### ** Answer: **

Given :

Here , a= 1, b= -3 and c =0

### ** Answer: **

Given :

Here , a=2, b= 5 and c =0

### ** Answer: **

Given :

Here , a= 3, b=0 and c =2

### ** Answer: **

Given :

Here , a=0, b= 1 and c = -2

### ** Answer: **

Given :

Here , a=2, b= 0 and c = -5

## ** NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.2 **

### ** Q1 ** Which one of the following options is true, and why? has

### (i) a unique solution,

### (ii) only two solutions,

### (iii) infinitely many solutions

### ** Answer: **

Given :

This equation is of a line and a line has infinite points on it and each point is a solution Thus, (iii) infinitely many solutions is the correct option.

** Q2 ** Write four solutions for each of the following equations:

### ** Answer: **

(i) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : .

(ii) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : .

(iii) Given :

Putting x=0, we have , means is a solution.

Putting x=1, we have , means is a solution.

Putting x=2, we have , means is a solution.

Putting x=3, we have , means is a solution.

The four solutions are : , , and .

** Q3 (i) ** Check which of the following are solutions of the equation and which are not: ((0,2)

### ** Answer: **

(i) Given :

Putting ,

we have ,

Therefore, is not a solution of .

** Q3 (ii) ** Check which of the following are solutions of the equation and which are not: (2,0)

### ** Answer: **

Given :

Putting (2,0),

we have ,

Therefore, (2,0) is not a solution of .

** Q3 (iii) ** Check which of the following are solutions of the equation and which are not: (4,0)

### ** Answer: **

Given :

Putting (4,0),

we have ,

Therefore, (4,0) is a solution of .

** Q3 (iv) ** Check which of the following are solutions of the equation and which are not:

### ** Answer: **

Given :

Putting ,

we have ,

Therefore, is not a solution of .

** Q3 (v) ** Check which of the following are solutions of the equation and which are not: (1,1)

### ** Answer: **

Given :

Putting (1,1) ,

we have ,

Therefore, (1,1) is not a solution of .

** Q4 ** Find the value of * k * , if , is a solution of the equation .

### ** Answer: **

Given :

Putting (2,1),

we have ,

Therefore, k=7 for putting x=2 and y=1.

## ** NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.3 **

### ** Q1 (i) ** Draw the graph of each of the following linear equations in two variables:

### ** Answer: **

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,4) and (1,3) are solutions of given equation.

** Q1 (ii) ** Draw the graph of each of the following linear equations in two variables:

### ** Answer: **

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,-2) and (1,-1) are solutions of given equation.

** Q1 (iii) ** Draw the graph of each of the following linear equations in two variables:

### ** Answer: **

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,0) and (1,3) are solutions of given equation.

** Q1 (iv) ** Draw the graph of each of the following linear equations in two variables:

### ** Answer: **

Given :

Putting x=0,we have

Putting x=1,we have

Thus, (0,3) and (1,1) are solutions of given equation.

### ** Answer: **

The equations of two lines passing through (2, 14) are given by :

There are infinite lines passing through (2, 14) because infinite lines pass through a point.

** Q3 ** If the point (3, 4) lies on the graph of the equation , find the value of * a * .

### ** Answer: **

Given : the point (3, 4) lies on the graph of the equation

Put x=3 and y=4

### ** Answer: **

Given: The distance covered as x km and total fare is Rs. y.

Total fare =the fare for first km + the fare of the remaining distance

For graph,

Putting x=0, we have

Putting x=1, we have

Putting x=2, we have

Hence,(0,3),(1,8) and (2,13) are solutions of equation.

The graph is as shown :

** Q5 (A) ** From the choices given below, choose the equation whose graph is given in Fig. 4.6.

### ** Answer: **

For the given figure :

Points on line are (-1,1) , (0,0 ) and (1,-1)

satisfies all the above points.

Thus, is the correct equation of the line.

** Q5 (B) ** From the choices given below, choose the equation whose graph is given in Fig. 4.7

### ** Answer: **

For the given figure :

Points on line are (-1,3) , (0,2 ) and (2,0)

satisfies all the above points.

Thus, is the correct equation of the line.

### ** Answer: **

Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0) , (0,5) and (2,10)

If diatance travelled is 2 units than work done is 10 units.

### ** Answer: **

Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0) , (0,5) and (2,10)

If diatance travelled is 0 units than work done is 0 units.

### ** Answer: **

Let the contribution of Yamini be x.

contribution of Yamini be y.

According to question,

For x=0 , we have

For x=10 , we have

For x=20 , we have

Hence, (0,100) , (10,90) and (20,80)

Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis.

### ** Answer: **

Let celsius be on x-axis and Fahrenheit be on y-axis.

For graph,

Putting x=0, we get

Putting x=5, we get

Putting x=10, we get

Hence, points are (0,32) , (5,41) and (10,50).

If the temperature is 30°C, what is the temperature in Fahrenheit?

### ** Answer: **

Put c=30,

Thus, the temperature = 30°C, then the temperature is 86 in Fahrenheit.

If the temperature is 95°F, what is the temperature in Celsius?

### ** Answer: **

Put F=95,

If the temperature is 95°F, then 35 is the temperature in Celsius.

### ** Answer: **

If the temperature is 0°C,

if the temperature is 0°F,

Thus, if the temperature is 0°C ,then temperature in fahrenheit is 32 and if the temperature is 0°F ,then temperature in celsius is -17.8 .

### ** Answer: **

Let temperature be x in both Fahrenheit and celsius.

Thus, 40 is the temperature which is numerically the same in both Fahrenheit and celsius.

## ** NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.4 **

** Q1 (i) ** Give the geometric representations of as an equation

in one variable

### ** Answer: **

Equation can be represented in one variable on number line.

** Q1 (ii) ** Give the geometric representations of as an equation: in two variables

### ** Answer: **

For 2 variable representation of .

Equation :

For graph,

x=0,we have y=3

x=1,we have y=3

x=2,we have y=3

Hence, (0,3) ,(1,3) and (2,3) are solutions of equation.

** Q2 (i) ** Give the geometric representations of as an equation: in one variable

### ** Answer: **

Equation can be represented in one variable on the number line.

The yellow mark represents x= - 4.5.

** Q2 (ii) ** Give the geometric representations of as an equation: in two variables

### ** Answer: **

For 2 variable representation of .

Equation :

For graph,

y=0,we have

y=1,we have

y=2,we have

Hence, , and are solutions of equation.

** NCERT solutions for class 9 maths chapter wise **

** NCERT solutions for class 9 subject wise **

** How to use NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables **

First of all, go through the conceptual text given in the NCERT textbook.

Then understand the application of concepts in the examples.

After this, you should come over practice exercises.

While practicing the exercises, you can use NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables as a reference.

After the completion of all the above points, you can practice the questions of past year papers.

* Keep Working Hard & Happy Learning! *

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

**Question: **What are the important topics in chapter Linear Equations in Two Variables ?

**Answer: **

Linear equations, solutions of linear equations, the graph of linear equation in two variables, equations of lines parallel to x-axis and y-axis are the important topics of this chapter.

**Question: **Is CBSE class 9 maths is tougher than CBSE class maths ?

**Answer: **

CBSE Class 9 maths is basically base for the CBSE class 10 maths. As some concepts are new some students may find it tougher but definitely it is not tougher.

**Question: **Does CBSE provides the solutions of NCERT for class 9 maths ?

**Answer: **

No, CBSE doesn’t provide NCERT solutions for any class or subject.

**Question: **Where can I find the complete solutions of NCERT for class 9 maths ?

**Answer: **

Here you will get the detailed NCERT solutions for class 9 maths by clicking on the link.

**Question: **How does the NCERT solutions are helpful ?

**Answer: **

NCERT solutions are provided in a very detailed manner which will give the conceptual clarity to the students. Also, they can take help from these solutions if they are not able to solve on their own

**Question: **Which is the official website of NCERT ?

**Answer: **

NCERT official is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

## Latest Articles

##### OFSS Bihar Admission 2020 Started on ofssbihar.in - Apply Now

OFSS Bihar admission 2020 Online - Bihar School Examination Bo...

##### Bihar Board Compartmental Result 2020 Declared!- Check BSEB 10...

Bihar Board Compartmental Result 2020 has released in on Aug 7...

##### NCERT Books for Class 11 English 2020-21 - Download Pdf here

NCERT Books for Class 11 English 2020-21 - NCERT books of Engl...

##### Mahadbt Scholarship 2020 -Dates, Eligibility, Application Form

Mahadbt Scholarship 2020 - Students can check eligibility, ben...

##### PRMO Registration 2020- Check Application Dates, Fee, Details

PRMO Registration 2020 - HBCSE will release the registration f...

##### Looking Ahead - Planning for Post COVID-19 Learning and Teachi...

Looking Ahead - Planning for Post COVID-19 Learning and Teachi...

##### Kerala Plus One Result 2020 Date and Time- Check DHSE Kerala ...

Kerala Plus One Result 2020 - DHSE, Kerala has declared the pl...

##### JAC Board 2021 - Jharkhand Academic Council Exam Date, Admit ...

Jharkhand Academic Council 2021 - JAC board has started 2020-2...

##### JAC 9th Syllabus 2020-21 - Download Jharkhand Board Class 9th ...

JAC Cass 9th Syllabus 2020-21 - Students can download Jharkhan...

##### Meghalaya Board of School Education 2021 - MBOSE Board Date Sh...

Meghalaya Board of School Education (MBOSE) 2021 - Know more d...